Information algebras of coherent sets of gambles in general possibility spaces
This work offers a theoretical link between imprecise probabilities and computer science formalisms, but it is incremental as it builds on existing frameworks without addressing a specific applied problem.
The paper embeds coherent sets of gambles into the algebraic structure of information algebra, providing a new perspective on the algebraic and logical structure of desirability and connecting imprecise probabilities to other formalisms in computer science.
In this paper, we show that coherent sets of gambles can be embedded into the algebraic structure of information algebra. This leads firstly, to a new perspective of the algebraic and logical structure of desirability and secondly, it connects desirability, hence imprecise probabilities, to other formalism in computer science sharing the same underlying structure. Both the domain-free and the labeled view of the information algebra of coherent sets of gambles are presented, considering general possibility spaces.